Where debating everything under the sun is only the beginning

Columbus thought the Earth was a lot smaller than it actually is, and he reached land right about where he expected to find it.

The circumference of the earth has been known since the ancient Greeks.

Is that actually true? The circumference of the earth has been known since the ancient Greeks

Not known, but guessed as best as they could    (well, estimated) And meanwhile Greek and Roman achievements were lost during the Middle Ages.

A lot of knowledge was lost between then and the time of Columbus. Even if the knowledge was known by some, it doesn't necessarily mean Columbus knew it. Reading Geography books takes a lot longer than googling "Earth circumference, if he could even find a book with that fact.

Columbus had sought an audience from the monarchs Ferdinand II of Aragon and Isabella I of Castile, who had united many kingdoms in the Iberian Peninsula by marrying, and were ruling together. On 1 May 1486, permission having been granted, Columbus presented his plans to Queen Isabella, who, in turn, referred it to a committee. After the passing of much time, the savants of Spain, like their counterparts in Portugal, replied that Columbus had grossly underestimated the distance to Asia. They pronounced the idea impractical and advised their Royal Highnesses to pass on the proposed venture.  (Emphasis mine.)

However, to keep Columbus from taking his ideas elsewhere, and perhaps to keep their options open, the Catholic Monarchs gave him an annual allowance of 12,000 maravedis and, in 1489, furnished him with a letter ordering all cities and towns under their domain to provide him food and lodging at no cost.[38]

Hmmm.... Allowing Columbus to set out on his venture could, then, have been a way to get rid of the pest.

In any case, his venture to reach the Far East by sailing West couldn't work because of the limited capacity of his ships to carry enough supplies for the voyage.

In other words, the experts of the medieval world were well aware of the true size of the earth (give or take a few 100 km), but it was ignored for political reasons.

Quote from: ersi on 2014-08-07, 17:28:25

Not known, but guessed as best as they could    (well, estimated) And meanwhile Greek and Roman achievements were lost during the Middle Ages.

I assume you're referring to Plato's guess, which was wildly off. I don't recall ever having read anything about his methods and if it might've been better with better data, but generically speaking if we want something more empirically founded we're going to have to look at Aristotle or later.

In any case, his venture to reach the Far East by sailing West couldn't work because of the limited capacity of his ships to carry enough supplies for the voyage.

So Columbus didn't know where he was going and didn't know where he was when he got there and didn't know where he had been when he got back.

So Columbus didn't know where he was going and didn't know where he was when he got there and didn't know where he had been when he got back.

how columbus convince the Monarch to fund his journey  ?

For instance, a book fell into the hands of the said Colombo, and he found it said in this book that at the end of the Western Sea [Atlantic] that is, on its western side, there were coasts and islands and all kinds of metals and also precious stones. The above-mentioned, having studied this book thoroughly, explained these matters one by one to the great of Genoa --- The above-mentioned Colombo saw that no help was forthcoming from the Genoese, he sped forth, went to the Bey of Spain [king], and told his tale in detail. --- In brief Colombo petitioned these people for a long time, finally the Bey of Spain gave him two ships...

Heyerdahl reported on his raft trip on the Pacific that food supplies were actually unnecessary. The ocean provided richly, fish climbed themselves on the raft to feed the crew, etc...

Perhaps a bigger problem than the quantity required for four months of fresh water is the fact that it might spoil.

I came across an interesting story about the science behind it: http://idlewords.com/2010/03/scott_and_scurvy.htm

(defun kaprekar-calculator (num)
    "Calculate the number of steps to Kaprekar's constant for a
  given four-digit number."
    (interactive "nGive a 4-digit number: ")
    (let* ((given (number-to-string (abs num)))
           (numlength (length given))
           (numstring (cond ((< 4 numlength)
                             (string-limit given 4))
                            ((> 4 numlength)
                             (concat (make-string (- 4 numlength) ?0)
                                     given))
                            (t given))))
      (require 'cl-lib)
      (if (equal (cl-sort numstring '>) (cl-sort numstring '<))
          (message "The given number must have at least two different digits")
        (if (equal "6174" numstring)
            (message "6174 is Kaprekar's constant!")
          (let ((result 0)
                (varstring numstring))
            (require 'calc)
            (while (not (equal "6174" varstring))
              (if (equal "999"
                         (calc-eval
                          (concat (cl-sort varstring '>)
                                  "-" (cl-sort varstring '<))))
                  (progn
                    (setq varstring "6174")
                    (setq result (+ 5 result)))
                (progn
                  (setq varstring
                        (calc-eval
                         (concat (cl-sort varstring '>)
                                 "-" (cl-sort varstring '<))))
                  (setq result (1+ result)))))
            (if (eq result 1)
                (message "%s resolves to Kaprekar's constant in one step"
                         numstring)
              (message "%s resolves to Kaprekar's constant in %d steps"
                       numstring result)))))))